I just did this quick little Q'n'A for Oxygen magazine...
Q: I want to increase weight for squats and deadlifts. What is the safest way to do it alone?
One little plate at a time.
Listen, unless you are want to become a powerlifter, there's no point in trying to lift maximum weights while alone. So train safe. But to get stronger, here's what to do.
Pick a repetition range, for example, 8-12 reps per exercise. Once you peak at the top end of the repetition range with PERFECT form, add 5% of the weight to the bar and drop down to the low end of the repetition range for your next workout. Work your way up - using only perfect form - until you can do 12 perfect reps. Then add weight and repeat.
Alternatively, consider using harder variations (split squats, front squats) that don't require heavy weights.
Don't forget about all of the dumbbell and bodyweight exercises in the Turbulence Training programs